2(x^2)-40x-400=0

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Solution for 2(x^2)-40x-400=0 equation: 


Simplifying
2(x2) + -40x + -400 = 0

Reorder the terms:
-400 + -40x + 2x2 = 0

Solving
-400 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-200 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-200 + -20x + x2 = 0

Solving
-200 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -20x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + -20x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -20x + x2 = 0 + 200
-20x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
-20x + x2 = 200

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 200 + 100

Reorder the terms:
100 + -20x + x2 = 200 + 100

Combine like terms: 200 + 100 = 300
100 + -20x + x2 = 300

Factor a perfect square on the left side:
(x + -10)(x + -10) = 300

Calculate the square root of the right side: 17.320508076

Break this problem into two subproblems by setting 
(x + -10) equal to 17.320508076 and -17.320508076.


Subproblem 1
x + -10 = 17.320508076

Simplifying
x + -10 = 17.320508076

Reorder the terms:
-10 + x = 17.320508076

Solving
-10 + x = 17.320508076

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = 17.320508076 + 10

Combine like terms: -10 + 10 = 0
0 + x = 17.320508076 + 10
x = 17.320508076 + 10

Combine like terms: 17.320508076 + 10 = 27.320508076
x = 27.320508076

Simplifying
x = 27.320508076


Subproblem 2
x + -10 = -17.320508076

Simplifying
x + -10 = -17.320508076

Reorder the terms:
-10 + x = -17.320508076

Solving
-10 + x = -17.320508076

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x = -17.320508076 + 10

Combine like terms: -10 + 10 = 0
0 + x = -17.320508076 + 10
x = -17.320508076 + 10

Combine like terms: -17.320508076 + 10 = -7.320508076
x = -7.320508076

Simplifying
x = -7.320508076


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.320508076, -7.320508076}
Solution
x = {27.320508076, -7.320508076}

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